Contributor info: Prof. Fabian Grusdt

Fabian Grusdt, Eugene Demler, Annabelle Bohrdt

SciPost Phys. 14, 090 (2023) · published 2 May 2023 | Toggle abstract · pdf

In strongly correlated quantum materials, the behavior of charge carriers is dominated by strong electron-electron interactions. These can lead to insulating states with spin order, and upon doping to competing ordered states including unconventional superconductivity. The underlying pairing mechanism remains poorly understood however, even in strongly simplified theoretical models. Recent advances in quantum simulation allow to study pairing in paradigmatic settings, e.g. in the $t-J$ and $t-J_z$ Hamiltonians. Even there, the most basic properties of paired states of only two dopants, such as their dispersion relation and excitation spectra, remain poorly studied in many cases. Here we provide new analytical insights into a possible string-based pairing mechanism of mobile holes in an antiferromagnet. We analyze an effective model of partons connected by a confining string and calculate the spectral properties of bound states. Our model is equally relevant for understanding Hubbard-Mott excitons consisting of a bound doublon-hole pair or confined states of dynamical matter in lattice gauge theories, which motivates our study of different parton statistics. Although an accurate semi-analytic estimation of binding energies is challenging, our theory provides a detailed understanding of the internal structure of pairs. For example, in a range of settings we predict heavy states of immobile pairs with flat-band dispersions - including for the lowest-energy $d$-wave pair of fermions. Our findings shed new light on the long-standing question about the origin of pairing and competing orders in high-temperature superconductors.

Claudius Hubig, Annabelle Bohrdt, Michael Knap, Fabian Grusdt, J. Ignacio Cirac

SciPost Phys. 8, 021 (2020) · published 6 February 2020 | Toggle abstract · pdf

Infinite projected entangled pair states (iPEPS) provide a convenient variational description of infinite, translationally-invariant two-dimensional quantum states. However, the simulation of local excitations is not directly possible due to the translationally-invariant ansatz. Furthermore, as iPEPS are either identical or orthogonal, expectation values between different states as required during the evaluation of non-equal-time correlators are ill-defined. Here, we show that by introducing auxiliary states on each site, it becomes possible to simulate both local excitations and evaluate non-equal-time correlators in an iPEPS setting under real-time evolution. We showcase the method by simulating the t-J model after a single hole has been placed in the half-filled antiferromagnetic background and evaluating both return probabilities and spin correlation functions, as accessible in quantum gas microscopes.

Fabian Grusdt, Zheng Zhu, Tao Shi, Eugene Demler

SciPost Phys. 5, 057 (2018) · published 5 December 2018 | Toggle abstract · pdf

Surprising properties of doped Mott insulators are at the heart of many quantum materials, including transition metal oxides and organic materials. The key to unraveling complex phenomena observed in these systems lies in understanding the interplay of spin and charge degrees of freedom. One of the most debated questions concerns the nature of charge carriers in a background of fluctuating spins. To shed new light on this problem, we suggest a simplified model with mixed dimensionality, where holes move through a Mott insulator unidirectionally while spin exchange interactions are two dimensional. By studying individual holes in this system, we find direct evidence for the formation of mesonic bound states of holons and spinons, connected by a string of displaced spins -- a precursor of the spin-charge separation obtained in the 1D limit of the model. Our predictions can be tested using ultracold atoms in a quantum gas microscope, allowing to directly image spinons and holons, and reveal the short-range hidden string order which we predict in this model.